Let p(x, y) be a propositional function if ꓯyꓱxp(x, y) is true does it necessarily follow that ꓱxꓯyp(x, y) is true? justify your answer or give a counter-example

Ok, we know that ꓯ y ꓱ x P(x,y) is true, and suppose we are working with integers.

Lets create a counter-example

if P(x,y) : x = y, then for all integer y you can find another integer x such the proposition is true, and ꓯ y ꓱ x P(x,y) is true.

now the second part; ꓱ x ꓯyP(x,y) is true? this means that exist an x, such that p(x,y) is true for all the y in the domain. Now, is also easy to se that, for each x, there is only one y that keeps the proposition true, and is y = x.

So ꓱx ꓯy P(x,y) is not true

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

the answer is -6

step-by-step explanation:

the answer is -6 because its next to the variable m